This invention generally relates to the transmission and receipt of data over telecommunications channels via the use of modems. More particularly, this invention relates to apparatus and methods for modem equilization which predistort data signals in a transmitter prior to sending the signals over a channel.
Data signals which are sent over a channel from a transmitter to a receiver are often corrupted by the inherent characteristics of the channel. Those inherent characteristics include the inability of a channel to provide a perfect response to a signal; i.e. the state of the channel at a previous moment in time affects the response of the channel at a later moment in time. In the art, this is known as intersymbol interference or ISI. In addition to ISI, data signals are also subjected to noise. Both the noise and ISI reduce the ability of a receiver to determine exactly what was transmitted from the transmitter.
In attempting to correct for ISI, it is common in the art to supply an equalizer in the receiver. The function of the equalizer is to correct for the ISI of the received signals so that the initial data can be recovered. With an equalizer in the receiver, typically, a known sequence of data signals (i.e. a training sequence) is sent from the transmitter to the receiver. Being that the data signal sequence itself is known, and the signals being received are known, it is possible for the equalizer first to determine the effects of the channel (i.e. the channel coefficients) on the transmitted signals, and then to compensate for those effects via any of several processes such as linear equalization or decision feedback equalization. Linear equalization functions by multiplying the incoming signals by the inverse of the ISI. While the ISI is generally removed from the incoming signals in this manner, noise inherent in the data transmission is undesirably simultaneously amplified. Additional details of linear equalization may be obtained by reference to Lee, Edward A. and Messerschmitt, David G., Digital Communication; (Kluwer Academic Publishers, 1988).
Decision feedback equalization avoids the noise amplification problems of linear equalization. However, in recreating the ISI via feedback, decision feedback equalization runs the risk of error propagation, as any decision errors that are made are fed back. Additional details of decision feedback equalization may be obtained by reference to Lee, Edward A. and Messerschmitt, David G., Digital Communication; (Kluwer Academic Publishers, 1988).
In response to the problems of linear and decision feedback equalization, M. Tomlinson, "New Automatic Equalizer Employing Modulo Arithmetic"; Electronics Letters Vol. 7, (March, 1971) pp. 138-139, suggested that equalization occur in the transmitter rather than in the receiver. In other words, the signals should be predistorted in the transmitter in such a manner that would cancel out the ISI of the channel upon transmission. As a result, after travel through the channel, the signals being received by the receiver would correspond to those signals which were generated by the transmitter prior to the predistortion, except for noise. The noise accompanying the data would not be amplified.
In more mathematical terms, if a series of data points r.sub.k are to be sent from the transmitter to the receiver, the Tomlinson scheme precodes the data according to a linear function: ##EQU2## where x.sub.k is the ISI corrected (i.e. predistorted) signal which is transmitted over the channel, r.sub.k is the precorrected selected signal point, and h.sub.i are the coefficients of a polynomial which describes the channel's impulse response (i.e. ISI).
While Tomlinson precoding is generally effective, the manner in which Tomlinson processes the signals prior to transmission causes signals having a desired power distribution which provides coding gain (e.g. as seen in U.S. Ser. Nos. 07/535,329 and 07/640,260 which are hereby incorporated by reference herein) to lose that gain. In other words, if the Tomlinson precoding is to be used, there is no benefit in providing a signal constellation having a desired "shape" or power distribution, as the Tomlinson precoding substantially destroys desired power distributions of coded signals. While for certain data transmission schemes this feature is acceptable, in high speed modems (e.g. 19.2 kbits/sec) it is advantageous that any gain available be maintained.
Recently, in Forney Jr., G. David, "Trellis Shaping", IEEE Information Theory Workshop, CCITT Study Group XVII & Working Parties, Geneva 15-23 Oct. 1990 (Temporary Document 211-E), an in Forney Jr., G. David, "Trellis Precoding: Combined Coding, Precoding and Shaping for Intersymbol Interference Channels", IEEE Information Theory Workshop, CCITT Study Group XVII & Working Parties, Geneva 15-23 Oct. 1990 (Temporary Document 212-E), Forney proposed an equalization scheme which avoids the drawbacks of both the equalization in the receiver, and the Tomlinson precoding methods. As set forth in the Forney articles, Trellis encoded and modulated data signals are predistorted to account for ISI in a manner which simultaneously provides minimum possible energy of the transmitted signal. While the Forney method theoretically provides excellent results, it has several drawbacks. First, the shaping scheme of Forney adds considerable delay to the process of transmitting data. Second, the Forney method requires very complex processing.